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December 1997 Superefficiency in nonparametric function estimation
Lawrence D. Brown, Mark G. Low, Linda H. Zhao
Ann. Statist. 25(6): 2607-2625 (December 1997). DOI: 10.1214/aos/1030741087

Abstract

Fixed parameter asymptotic statements are often used in the context of nonparametric curve estimation problems (e.g., nonparametric density or regression estimation). In this context several forms of superefficiency can occur. In contrast to what can happen in regular parametric problems, here every parameter point (e.g., unknown density or regression function) can be a point of superefficiency.

We begin with an example which shows how fixed parameter asymptotic statements have often appeared in the study of adaptive kernel estimators, and how superefficiency can occur in this context. We then carry out a more systematic study of such fixed parameter statements. It is shown in four general settings how the degree of superefficiency attainable depends on the structural assumptions in each case.

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Lawrence D. Brown. Mark G. Low. Linda H. Zhao. "Superefficiency in nonparametric function estimation." Ann. Statist. 25 (6) 2607 - 2625, December 1997. https://doi.org/10.1214/aos/1030741087

Information

Published: December 1997
First available in Project Euclid: 30 August 2002

zbMATH: 0895.62043
MathSciNet: MR1604424
Digital Object Identifier: 10.1214/aos/1030741087

Subjects:
Primary: 62G07
Secondary: 62B15, 62G20, 62M05

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.25 • No. 6 • December 1997
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